Diffusion of Linear and Branched C7 Paraffins in ITQ-1 Zeolite. A

Aug 20, 1998 - Hernandez, E.; Kawano, M.; Shubin, A. A.; Freeman, C. M.; Catlow, C. R. A.; Thomas, J. M.; Zamaraev, K. I. 9th International Zeolite Co...
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J. Phys. Chem. B 1998, 102, 7085-7090

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ARTICLES Diffusion of Linear and Branched C7 Paraffins in ITQ-1 Zeolite. A Molecular Dynamics Study Avelino Corma,*,† C. Richard A. Catlow,‡ and German Sastre† Instituto de Tecnologia Quimica U.P.V.-C.S.I.C., UniVersidad Politecnica de Valencia, AVenida Los Naranjos s/n, 46022 Valencia, Spain, and DaVy Faraday Research Laboratory, The Royal Institution of Great Britain, 21 Albemarle Street, W1X 4BS London, U.K. ReceiVed: February 26, 1998

Molecular dynamics techniques have been used to simulate the diffusion of n-heptane and 2-methylhexane in purely siliceous ITQ-1 zeolite, a microporous solid with two independent channel systems of 10 MR (interconnected sinusoidal channels) and 12 MR (interconnected large cavities). Two hundred picosecond runs at a temperature of 450 K were performed in order to characterize the diffusion features of these hydrocarbons. In the 10 MR sinusoidal system, the n-heptane diffuses rather freely through the channels whereas the 2-methylhexane is stuck at the pore entrances. Diffusion through the 12 MR large cavities is dominated by intracage motion due to the presence of preferential minimum energy positions at the top of the 12 MR pockets. Implications for reactivity and selectivity in cracking and isomerization reactions are drawn from the results.

1. Introduction The synthesis of new microporous materials with pore systems containing 10 and 12 MR pores and/or cavities opens new possibilities for the applications of zeolites in the oil industry.1-3 One of these zeolites is MCM-22, whose IZA code is MWW.4 This structure contains two independent pore systems formed by interconnected sinusoidal 10 MR pores with a 4-5.5 Å diameter, and an independent 12 MR system formed by large cages of 18.2 × 7.1 Å connected between them and with the external surface through 10 MR windows (Figure 1). The MWW zeolite can be synthesized with framework Si/Al ratios below 150 using hexamethylene-imine as template by following the original procedure reported in the patent literature5 or for Si/Al above that ratio up to the pure silica form, the resultant material being named as ITQ-1.6 ITQ-1 has been synthesized in the absence of alkaline ions and using 1,2 dimethyladamantane ammonium and hexamethylene-imine as structure directing agents. The use of zeolites as catalysts, and their advantages over amorphous silica alumina, is to a large extent based on their microporous crystalline structure, which allows a shape selective control of the guest molecules penetrating the structure. The selectivity is one of the main concerns in designing new catalysts suited to specific reactions, and the structural variety of zeolites4 offers many possibilities for a wide range of chemical reactions. Finding the best structure for a given reaction can be ac* To whom correspondence should be sent. † Universidad Politecnica de Valencia. ‡ The Royal Institution of Great Britain.

complished in part by inspecting the pore and channel dimensions of the zeolite, as well as its microporous topology. All the potential acid sites generated when introducing framework Al in the MWW topology can be reached through either the 10 or 12 MR channels and cavities, except one that points to the 10 MR channels. If one takes into account the very different void spaces existing in the 10 and 12 MR channels, it appears that the catalytic behavior of this material will be highly dependent on the relative diffusivities of a given molecule in the two systems of pores. In other words, when a molecule can diffuse through the two pore systems, the final selectivity will be mainly dictated by the pore system in which the molecule stays longer. Thus in the case of the MWW zeolite, the presence of the large 12 MR cages together with the independent circular 10 MR channel represents a very interesting model for an extreme topological arrangement that combines the diffusion in medium size channels with intra- and intercage diffusivity in the large pores. Several methods have been used to measure experimentally the diffusion of hydrocarbons in zeolites,7-9 and in this way average diffusivities can be obtained in zeolites with complex pore structures including 10 and 12 MR pores in the same structure. However, it should be possible by using molecular dynamics techniques not only to study the dynamic behavior of a molecule in a zeolite10-15 but also to establish the different diffusion patterns occurring when pores of different dimensions are present in a given structure.16 The quality of these simulations rests mainly in the models defining the zeolite and the diffusing hydrocarbons, the quality of the interatomic potentials employed, and also the time of the simulation. The

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Figure 1. Schematic view of the two independent void systems in ITQ-1. The sinusoidal 10 MR channels are all interconnected to each other, and they allow multiple trajectories to be followed by the diffusing molecules. The large cavities are 12 MR in cross-section size and are interconnected through short 10 MR conducts around 3 Å long. Each large cavity contains six 10 MR windows.

recent advent of parallel computing has greatly enhanced the possibility of performing more realistic simulations in this respect.17 In the present paper we have chosen two molecules, n-heptane and 2-methylhexane, which are of practical interest to increase the octane number of the final gasoline as well as to increase the amount of C3 and C4 olefins in FCC units, where shape-selective cracking reactions are involved.18-22 Thus, the diffusion of those molecules in the two independent pore systems has been simulated using molecular dynamics techniques in the purely siliceous ITQ-1 zeolite at a temperature of 450 K. From our results, intracage, intercage, and pore diffusivity behavior have been established and implications on reactivity have been drawn. 2. Methodology Atomistic periodic molecular dynamics calculations have been carried out to simulate the diffusion of n-heptane and 2-methylhexane in purely siliceous ITQ-1. The general purpose DL_POLY_2.023 parallel code was used throughout this study. The Verlet algorithm24 has been used to solve the classical equations of motion after initial velocities have been assigned to all atoms of the system according to a temperature-dependent Maxwell-Boltzmann distribution. The system comprises a 2 × 2 × 2 macrocell of ITQ-1 (1728 atoms) and 12 molecules of the C7 paraffin (276 atoms) located inside the macrocell. Two different simulations have been performed: one with 12 molecules of n-heptane and the other with 12 molecules of 2-methyl-hexane as the diffusing hydrocarbon. In each simulation, six molecules have been placed in the 10 MR sinusoidal system and six molecules in the 12 MR supercage void system. From the computational point of view, the advantage of having two independent void systems is that we can study the hydrocarbon diffusion in each one of the systems simultaneously without the need to perform two separate runs, saving therefore a large amount of CPU time. After each of the runs has been carried out (one with n-heptane and the other with 2-methylhexane), the diffusion features in each void system are obtained

independently. The resultant overall loading in the simulations corresponds to 1.5 molecules/u.c., and this concentration in turn is distributed 50% in each of the independent void systems as explained above. Time steps of 1 fs and an equilibration temperature of 450 K have been used in all the present simulations. During the equilibration stage 20 ps runs were performed to ensure that the energy was stationary, and thereafter the simulations were additionally extended over 200 ps within the NVE ensemble. Periodic boundary conditions were applied to the macrocell system. History files were saved every 1 ps, and from these, data analysis of the diffusion process were carried out. Explicit dynamical treatment of all the atoms of the systems 2004 in totalswas included in the simulation. Although this increases substantially the computational expense, such a task was feasible using the DL_POLY code in its fully parallelized implementation on the 512 PE CRAY-T3D MPP computer at the EPCC (Edinburgh Parallel Computing Centre). The present simulations were run using 64 processors, and the efficiency of the parallel code in the present simulations is close to 65%. The computer time used to complete all the simulations was about 200 × 64 h. Four types of interatomic potentials are needed to model this system:

Vtotal ) Vzeolite + Vhydrocarbon + Vhydrocarbon-hydrocarbon + Vzeolite-hydrocarbon (1) The potentials employed for the zeolite framework, Vzeolite,25 the sorbate, Vhydrocarbon,26 and the sorbate-sorbate and frameworksorbate, Vhydrocarbon-hydrocarbon, Vzeolite-hydrocarbon,25 have been already used in a previous study where more details of the MD techniques employed and the potential parameters are found.16 Two different atom types are considered in the hydrocarbon molecules: C and H. A total of 22 bond terms, 42 angle terms, and 54 dihedral-angle terms are employed to describe the hydrocarbon molecules. Partial charges of -0.16 for C and

Diffusion of C7 Paraffins in ITQ-1 Zeolite

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Figure 2. General features of diffusing molecules through ITQ-1. (A) A molecule diffuses through the 10 MR sinusoidal channel system. (B) Potential energy minima in the sinusoidal channels. (C) Potential energy minima in the large cavities. (D) Intracage motion in the large cavities around one minimum. (E) Intracage motion in the large cavities around the two minima. (F) Intercage diffusion through the large cavities.

+0.07 for H were used for the Coulombic interactions. Formal charges are considered in the zeolite framework.

Figure 3. Mean square displacement (MSD) plots of n-heptane (solid line) and 2-methylhexane (dotted line) in ITQ-1. The plot shows the greater diffusivity of the smaller n-heptane with respect to 2-methylhexane, which, in turn, shows no diffusion owing to the steric hindrance in the sinusoidal channels.

3. Results and Discussion A careful look at the void spaces present in MCM-2227 (Figure 1) reveals some of its special features that will affect diffusion of hydrocarbons through the structure. First, all the sinusoidal channels intersect with each other and have a high degree of tortuosity. Although linear hydrocarbons diffuse without particular restrictions through sinusoidal channels, large linear hydrocarbons could be somewhat affected by the tortuosity of the 10 MR system in MCM-22. Second, although the large cavities are expected to host both linear and branched C7 hydrocarbons, it will be of interest to compare the relative mobility and location of each isomer inside the cage. Additionally, we are also interested in knowing whether the hydrocarbons cross from one cavity to other through the 10 MR openings or tend to remain inside a given cavity. Diffusion features such as the ones graphically described in Figure 2 represent general possibilities whose occurrence in our particular case has to be either confirmed or ruled out by the simulations. Obviously, all these features will depend on factors such as temperature and loading. Although we have performed all of our simulations at the same loading and temperature, conclusions regarding selectivity will stem from the results. 3.1. Diffusion of 2-Methylhexane in ITQ-1. The first simulation was carried out with an initial configuration of six molecules of 2-methyl-hexane in the sinusoidal system and six molecules of 2-methyl-hexane in the large cage system. These molecules were placed inside the 2 × 2 × 2 ITQ-1 macrocell giving a loading that in principle allows the molecules to cross from one large cavity to another and also diffuse rather freely through the sinusoidal system, without too many interactions between the diffusing molecules. From the 200 ps run at the temperature of 450 K, the mean square displacement (MSD) plot (Figure 3) and the trajectories of the center of mass of 2-methyl-hexane molecules (Figure 4) are obtained. These trajectories are projected into a Cartesian reference system inwhich the z direction corresponds to the crystallographic [001] direction. Over the reference system, a schematic depiction of the channels is superimposed to make easy the understanding of the diffusion process. The diffusion features in this case can be fully visualized with the aid of the yx and zy projections (Figure 4). Diffusion through the 10 MR sinusoidal channels can be better observed in the yx projection because these channels are perpendicular to the z axis (Figure 4). Molecules labeled from

Figure 4. 2-Methylhexane trajectories obtained from the 200 ps run. Projections in xy and yz are shown. The crystallographic [001] direction is coincident with the Cartesian z axis. Diffusion through the 10 MR sinusoidal system can be better appreciated across the xy projection. Diffusion in the large cavities can be better appreciated across the yz projection. The trajectories correspond to the center of mass of the n-heptane. A schematic view of the ITQ-1 void systems is superimposed along with the trajectories to visualize better the diffusion features. Molecules labeled from 1 to 6 are located in the 10 MR channels, and molecules labeled from 7 to 12 are located in the 12 MR supercage system.

1 to 6 occupy these channels. We can see that 2-methyl-hexane molecules in these channels are stuck, and they cannot diffuse through the sinusoidal channels. They only remain in a very

7088 J. Phys. Chem. B, Vol. 102, No. 37, 1998 local part of the channel around its initial configuration. Very occasionally, we see a slight mobility as occurs to molecule 6, which makes a short move (around 5 Å) from one position of minimum potential energy to another. Such positions (marked as B in Figure 2) seem to be located close to the intersecting space between the bends of the sinusoidal channels. There is hence a restricted diffusion phenomena, which in the case of the trajectories (Figure 4) is shown clearly in what we called in a previous work extensiVe local motion,16 meaning that the molecules move most of the time around a very restricted part of the solid. More surprising seems to be the diffusion features shown by 2-methyl-hexane molecules located inside the large cavities, which are labeled from 7 to 12 in Figure 3. Although one may initially think of a larger mobility in the cavities, we see that the molecules prefer to locate also in a rather restricted part of the solid. In this case, the diffusion features can perhaps be better appreciated in the zy projection (Figure 4). There we can see that 2-methyl-hexane molecules spend most of their time in a restricted part of the supercage. Although we believe these supercages to have space enough to allow a larger diffusivity of the branched C7 alkane, there seems to be a relatively deep well of potential that causes the molecule to stay around the minimum potential energy location. The present study allows us to test whether this is the case or, on the other hand, this extensive local motion is due to steric restrictions imposed by the size of the branched alkane with respect to the large cavity. We achieve this by comparing these trajectories with the mobility of the less impeded linear alkane in the cavity. If the low mobility is due to a potential well, then this will also be present for the linear hydrocarbon. Alternatively, if the low mobility of the 2-methyl-hexane is due to steric factors, then it will not be shown by the linear hydrocarbon, which can certainly fit very loosely in the large cavity. We will return to this later. It is also noted from Figure 4 that it is possible for the 2-methyl-hexane molecules to move through the cavity, as is noted by the diffusion path of molecule 8, which moves around 10 Å through the longitudinal direction in the large cavity. This is also noted for molecule 11 although this excursion is shorter than in the case of molecule 8. In both cases (molecules 8 and 11) it can be observed from Figure 4 that 2-methyl-hexane spends most of its time near the minimum potential energy location, and from the history files, we find that the time spent by these molecules off the minimum is only 8 and 4 ps, respectively, out of a total of 200 ps simulation time. The trajectory graphs also show that no one molecule migrates from one cavity to another through the 10 MR openings. This somewhat surprising feature of the diffusion of 2-methyl-hexane in the large cavities has also to be rationalized taking into account the temperature selected for the runs. At 450 K the average kinetic energy of the 2-methyl-hexane molecules does not seem to be high enough to activate a larger diffusion path. It has to be remarked that we do not rule out the possibility of 2-methylhexane molecules crossing from one cavity to another at this temperature. However, we can assert that this is not a very frequent event at this temperature. Increasing the time of simulation will possibly allow us to observe some of these rather rare intercage diffusion events. Obviously this finding has important consequences in the field of reactivity because the occurrence of cracking and some cracking-derived reactions will possibly change noticeably when the temperature increases so as to allow a larger diffusivity of the C7 branched hydrocarbons through the void space of the large cavities. Also, the location of the potential active centers in the cavities will play a crucial

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Figure 5. n-Heptane trajectories obtained from the 200 ps run. Projections in xy and yz are shown. The crystallographic [001] direction is coincident with the Cartesian z axis. Diffusion through the 10 MR sinusoidal system can be better appreciated using the xy projection. Diffusion in the large cavities can be better appreciated using the yz projection. The trajectories correspond to the center of mass of the 2-methylhexane. A schematic view of the ITQ-1 void systems is superimposed along with the trajectories to visualize better the diffusion features. Molecules labeled from 1 to 6 are located in the 10 MR channels, and molecules labeled from 7 to 12 are located in the 12 MR supercage system.

role, and the final reactivity will depend on whether they are or are not located near the minimum potential energy position. From our results we also find that diffusion of C7 branched hydrocarbons is very highly impeded along the sinusoidal 10 MR channels, owing to steric constraints. 3.2. Diffusion of n-Heptane in ITQ-1. The MSD plot (Figure 3) and the trajectories corresponding to the 200 ps run at 450 K (Figure 5) have been obtained from the simulation run. The comparison of the MSD plots for the two isomers allows us to visualize the larger diffusivity of the n-heptane with respect to the 2-methyl-hexane. Even though the statistics do not show us a linear plot, the qualitative conclusion regarding relative diffusivities can be drawn. Additionally, the serious steric hindrance of the 2-methyl-hexane in the sinusoidal channels prevents the isomer from diffusing, as can also be appreciated from the MSD plot (Figure 3). As in the previous case, six molecules have been placed in each of the void systems. First, we can look to the trajectories of the n-heptane molecules located in the sinusoidal system, which are labeled from 1 to 6. Again, for this diffusion path, the projection on yx shows with more clarity the paths followed by the molecules. We can see (Figure 5) a tremendous difference with respect to the branched hydrocarbon. In this

Diffusion of C7 Paraffins in ITQ-1 Zeolite case, the graph shows how the molecules have no restriction whatsoever for the diffusion through the sinusoidal channels. The molecules go from one channel to other through their intersection without apparent activation energy, showing no preferential location along the channels. One of the main features of these channels is their large number of intersections they have. This strongly influences diffusion since in the case of relatively high loading, when one molecule is “obstructing” any part of the channel system, a second molecule can take an alternative route without them intercepting each other in their trajectories, owing to the possibility of having many alternative routes for the diffusion path. This has implications in reactivity since it allows there to be a considerable loading without limiting the access of molecules to the active centers. On the other hand, the restricted dimensions of this channel system has the feature that will allow relatively high loading of molecules such as n-alkanes and n-olefins without giving an appreciable occurrence of bimolecular reactions, owing to the fact that the void system is not large enough to accommodate the corresponding transition states. This can be relevant when using MCM-22 as a FCC additive, in which the cracking/oligomerization and cracking/ hydrogen transfer ratios have to be maximized. Another consideration that can be derived from our simulations is that despite the high degree of tortuosity exhibited by these channels, there seems to be no impediment for C7 linear hydrocarbons to diffuse. It is obvious that the rotational capability of this molecule (around the C-C-C-C dihedral angles) is fast enough to avoid any restriction on the mobility of the molecules. If we now look (Figure 5) at the n-heptane molecules located in the large cavities, which are labeled from 7 to 12, the same behavior that was previously observed with the branched hydrocarbon is seen. In other words, the same extensive local motion features are observed here despite the fact that the n-heptane molecules pose less steric hindrance on the mobility inside the large cavities. This confirms our previous conclusion that this behavior is due to the existence of a minimum in the potential energy surface that makes also the n-heptane molecules, as was the case in 2-methyl-hexane molecules, occupy a site near the minimum energy position. In this case no migration phenomena from one minimum to the other in the large cavity is observed unlike in the case of the branched hydrocarbon. This result confirms that intracage migration, as shown in Figure 2E, is infrequent at this temperature. Also, as in the branched hydrocarbons, none of the molecules happen to cross from one large cavity to another through the 10 MR openings. Crossing from one cavity to another is expected to occur for n-heptane at higher temperatures, and possibly this will show differences between n- and branched alkanes. Although this is only an hypothesis, the results of the simulation allow one to raise this question owing to the differences observed in the diffusion through the 10 MR sinusoidal channels, which is expected to correlate with the intercage motion since they are connected through similar 10 MR openings. Given this behavior, then it may well occur that in a certain range of temperatures, the linear C7 hydrocarbon molecules would already have the activation energy necessary to cross from one large cavity to another, while almost none of the branched C7 hydrocarbons would. In this way a double selectiVity effect would be present: with respect to linear/branched hydrocarbons and with respect to each of the void systems in MCM-22. 4. Conclusions MWW zeolite presents a unique void system that can certainly be exploited in industrial applications, especially those involving

J. Phys. Chem. B, Vol. 102, No. 37, 1998 7089 C6-C9 hydrocarbon transformations. Our dynamic framework periodic molecular dynamic simulations of diffusion of nheptane and 2-methyl-hexane in the pure silica ITQ-1 show how trajectory analysis of 200 ps runs at a temperature of 450 K can be used to characterize the diffusion features of these two hydrocarbons over the two independent void systems present in this zeolite. Diffusion of 2-methyl-hexane through the 10 MR sinusoidal system presents serious steric restrictions, which make the molecules stick to the minimum energy locations of the channels. A slightly different picture appears for the branched alkane in the larger cavities in which, although extensive local motion is still the dominant feature, the larger void spaces together with the presence of some larger mobilities indicate that the process is activated and therefore larger mobilities will be expected at higher temperatures. We have found two important minima of potential energy inside the large cavities, which make the smaller n-heptane behave in a very similar way toward the diffusion in this void system. It is expected that the smaller size of the linear C7 alkane will make it possible for this molecules to cross from one large cavity to another, i.e., intercage diffusion, as the temperature increases. The linear n-heptane shows a very different picture with respect to the branched isomer regarding diffusion through the sinusoidal 10 MR channel, the former diffusing without any steric restriction. Also, the abundance of alternative paths for the diffusion in the sinusoidal system will make possible diffusion without important restrictions at relatively high loading, which can be important in terms of the number of molecules that can undergo the catalytic reaction. Temperature can be possibly tuned together with the number and location of active sites in MCM-22 in order to find the most suitable linear/branched reactivity ratio to match the specific targets for the desired process, taking advantage of the different diffusion features of linear and branched hydrocarbons obtained from the simulations. Acknowledgment. G.S. thanks Ministerio de Educacion y Ciencia of Spain for a postdoctoral research grant. We thank Dr. W. Smith for useful discussions regarding DL_POLY code. The EPCC (Edinburgh Parallel Computer Centre) and the EPSRC funded CRAY-T3D Materials Chemistry Consortium are gratefully acknowledged. References and Notes (1) Corma, A.; Davis, M.; Fornes, V.; Gonzalez-Alfaro, V.; Lobo, R.; Orchilles, A. V. J. Catal. 1997, 167, 438. (2) Corma, A.; Martinez-Triguero, J. J. Catal. 1997, 165, 102. (3) Corma, A.; Gonzalez-Alfaro, V.; Orchilles, A. V. Appl. Catal. A 1995, 129, 203. (4) Meier, W. M.; Olson, D. H.; Baerlocher, Ch. Atlas of Zeolite Structure Types, 4th ed.; Elsevier: Amsterdam, 1996. (5) Rubin, M. K.; Chu, P. U.S. Patent 4954325, 1990. (6) Camblor, M. A.; Corell, C.; Corma, A.; Diaz-Caban˜as, M. J.; Nicopoulos, S.; Gonzalez-Calbet, J. M.; Vallet-Regi, M. Chem. Mater. 1996, 8, 2415. (7) Ka¨rger, J.; Caro, J. J. Chem. Soc., Faraday Trans. 1977, 1363. (8) Jobic, H.; Bee, M.; Caro, J. Bu¨llow, M.; Ka¨rger, J. J. Chem. Soc., Faraday Trans. 1989, 85, 4201. (9) Ka¨rger, J.; Ruthven, D. M. Zeolites 1989, 9, 267. (10) Hernandez, E.; Kawano, M.; Shubin, A. A.; Freeman, C. M.; Catlow, C. R. A.; Thomas, J. M.; Zamaraev, K. I. 9th International Zeolite Conference; von Ballmoos, R., Higgins, J. B., Treacy, M. M. J., Eds.; Butterworth-Heinemann, Boston, MA 1993; p 695. (11) Kawano, M.; Vessal, B.; Catlow, C. R. A. J. Chem. Soc., Chem. Commun. 1992, 879. (12) Klein, H.; Fuess, H.; Schrimpf, G. J. Phys. Chem. 1996, 100, 11101. (13) Santilli, D. S.; Harris, T. V.; Zones, S. I. Microporous Mater. 1993, 1, 329. (14) Santilli, D. S.; Zones, S. I. Catal. Lett. 1990, 7, 383. (15) Yashonat, S.; Bandyopadhyay, S. Chem. Phys. Lett. 1994, 228, 284.

7090 J. Phys. Chem. B, Vol. 102, No. 37, 1998 (16) Sastre, G.; Raj, N.; Catlow, C. R. A.; Roque-Malherbe, R.; Corma, A. J. Phys. Chem. B 1998, 102, 3198. (17) Catlow, C. R. A. Proceedings of the Royal Institution; 1996; Vol. 67, Chapter 5. (18) Chen, N. Y.; Garwood, W. E.; Dwyer, F. G. In Shape SelectiVe Catalysis in Industrial Applications; Dekker: New York, 1989. (19) Maxwell, I. E. CATTECH, March 1997. (20) Corma, A.; Martinez, A. AdV. Mater. 1995, 7, 137. (21) Abbot, J.; Wojciechowski, B. W. Can. J. Chem. Eng. 1985, 63, 462.

Corma et al. (22) Buchanan, J. S.; Santiesteban, J. G.; Haag, W. O. J. Catal. 1996, 158, 279. (23) Smith, W.; Forester, T. R. J. Mol. Graphics 1996, 14, 136. (24) Verlet, L. Phys. ReV. 1967, 159, 98. (25) Catlow, C. R. A.; Freeman, C. M.; Vessal, B.; Tomlinson, S. M.; Leslie, M. J. Chem. Soc., Faraday Trans. 1991, 87, 1947. (26) Oie, T.; Maggiora, T. M.; Christoffersen, R. E.; Duchamp, D. J. Int. J. Quantum Chem., Quantum Biol. Symp. 1981, 8, 1. (27) Leonowicz, M. E.; Lawton, J. A.; Lawton, S. L.; Rubin, M. K. Science 1994, 264, 1910.